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Triangle Inequality Theorem Worksheet

Explore the Triangle Inequality Theorem with this worksheet, featuring questions on determining valid triangle side lengths and applying the theorem to solve problems.

Grade 9 Math GeometryTriangle Inequality Theorem
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Includes

Multiple ChoiceFill in the BlanksShort AnswerTrue / FalseMatching

Standards

CCSS.MATH.CONTENT.HSG.CO.C.10

Topics

mathgeometrytriangleinequalitygrade 9
7 sections · Free to use · Printable
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Triangle Inequality Theorem

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. Which of the following sets of side lengths can form a triangle?

a

3 cm, 4 cm, 8 cm

b

5 cm, 7 cm, 12 cm

c

6 cm, 9 cm, 10 cm

d

2 cm, 3 cm, 5 cm

2. If two sides of a triangle are 10 inches and 15 inches long, which of the following could be the length of the third side?

a

4 inches

b

25 inches

c

5 inches

d

20 inches

3. The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be   than the length of the third side.

4. If a triangle has sides of length 'a', 'b', and 'c', then it must be true that a + b > c, a + c > b, and  .

5. A triangle has two sides with lengths 7 cm and 11 cm. What is the range of possible lengths for the third side?

6. Can a triangle be formed with side lengths 14 mm, 6 mm, and 8 mm? Justify your answer using the Triangle Inequality Theorem.

7. A triangle with side lengths 1 cm, 2 cm, and 3 cm can exist.

T

True

F

False

8. If the sum of two sides of a triangle is equal to the third side, it forms a degenerate triangle.

T

True

F

False

Match the side lengths with whether they can form a triangle or not.

9. 5, 5, 5

 

a. Cannot form a triangle

10. 1, 2, 4

 

b. Can form a triangle

11. 10, 10, 20

 

c. Can form an equilateral triangle